A. 32 cu ft B. 49 cu ft C. 57 cu ft D. 1,145 cu ft. F. 96 sq in. G. 136 sq in. H. 192 sq in. J. 272 sq in. 5 in
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1 7.5 The student will a) describe volume and surface area of cylinders; b) solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and c) describe how changing one measured attribute of a rectangular prism affects its volume and surface area. HINTS & NOTES **Use the formula sheet at all times** Use the formulas exactly as they are on the sheet. Don t forget to check the units: Squared units for area and cubed units for volume. Surface area amount needed to cover something Volume amount needed to fill something PRACTICE 1. A cylinder-shaped can has a diameter of 4 feet and a height of 4.5 feet. If the can is empty, which is closest to the minimum amount of water needed to completely fill the can? A. 32 cu ft B. 49 cu ft C. 57 cu ft D. 1,145 cu ft 2. Lindsay is wrapping a birthday gift in a rectangular prism-shaped box with gift wrap. Changing Attributes There is a direct relationship between changing one measured attribute of a rectangular prism by a scale factor and its volume. For example, doubling the length of a prism will double its volume. This direct relationship does not hold true for surface area. What is the minimum amount of gift wrap Lindsay needs to cover the entire box? F. 96 sq in. G. 136 sq in. H. 192 sq in. J. 272 sq in. 3. This rectangular prism is built with 1-inch cubes. What is the volume? A. 10 in. 3 B. 20 in. 3 C. 40 in. 3 D. 80 in. 3 5 in 8 in 2 in 4. Crunch and Munch cereal is designing a new box. How much cardboard is needed to create the box if the height is 4 cm., the length is 5 cm., and the width is 2.5 cm.? F. 23 cm. 2 G cm. 2
2 H. 50 cm. 2 J. 85 cm Find the volume of a rectangular prism with a length of 6 in., width of 2 in., and height of 4 in. A. 12 in. 3 B. 24 in. 3 C. 48 in. 3 D. 64 in The volume of this prism is 960 cubic inches, what is the height? 7. Keith has is thinking about creating a cube that measures 5 cm per edge. Describe the volume of this cube in comparison to a cube with 10 cm per edge. Use the space below for your answer.
3 Skills Checklist I can Determine if a practical problem involving a rectangular prism or cylinder represents the application of volume or surface area. Find the surface area of a rectangular prism. Solve practical problems that require finding the surface area of a rectangular prism. Find the surface area of a cylinder. Solve practical problems that require finding the surface area of a cylinder. Find the volume of a rectangular prism. Solve practical problems that require finding the volume of a rectangular prism. Find the volume of a cylinder. Solve practical problems that require finding the volume of a cylinder. Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be limited to changing attributes by scale factors only. Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be limited to changing attributes by scale factors only. 7.6 The student will determine whether plane figures quadrilaterals and triangles are similar and write proportions to express the relationships between corresponding sides of similar figures. HINTS & NOTES PRACTICE Similar figures same shape but different size. Their corresponding angles have the same measure and their corresponding proportional. This means that the ratios of corresponding equal. Remember to solve a proportion cross multiply. The symbol ~ means is similar to. 1. Triangle FOX is similar to triangle FAN. Which side of the triangle FOX corresponds to side FA? A. B. C. D. NX FO AO FN 2. Which of these is a set of similar polygons? F. all rectangles G. all trapezoids H. all right triangles J. all equilateral triangles 3. ABC is similar to XYZ. AB = 15 and XY = 25. If YZ = 15, what is the measure of BC?
4 A. 5 B. 9 C. 10 D Find x for each set of similar figures below. a. b. 5. Select all the true statements regarding the similar figures represented below.
5 6. If ΔABC is similar to ΔADE, then AB AD =? AE. Which segment replaces the? to make the statement true? Write the segment name in the box. Skills Checklist I can Identify corresponding sides and corresponding and congruent angles of similar figures using the traditional notation of curved lines for the angles. Write proportions to express the relationship between the lengths of corresponding sides of similar figures. Determine if quadrilaterals or triangles are similar by examining congruence of corresponding angles and proportionality of corresponding sides. Given two similar figures, write similarity statements using symbols such as ΔABC ~ ΔDEF, A corresponds to D, and AB corresponds to DE. 7.7 The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid. HINTS & NOTES PRACTICE Quadrilateral polygon w/ 4 1. sides Quadrilateral Parallelogram Properties congruent (equal in length) parallel If all four angles of the polygon pictured measure 90 o, then the polygon is most likely a A. square B. rhombus C. rectangle D. nonagon 2. If all sides of the polygon pictured are NOT equal in length, the polygon is most likely a F. rectangle G. parallelogram
6 angles are congruent (equal in measure) H. trapezoid J. rhombus 3. Which polygon is NOT a quadrilateral? Rectangle Square Rhombus Trapezoid congruent (equal in length) parallel all four interior angles measure 90 o (right angles) parallel all four equal all four interior angles measure 90 o (right angles) parallel all four equal one pair of opposite parallel and the other pair are not 4. Identify all the possible classifications of the figure provided, given its characteristics. 5. Quadrilateral ABCD is a parallelogram. Which two segments must be parallel? A. AB andcd B. AB and BC C. AB and DA D. AC and BD 6. How are a square and a rhombus alike?
7 F. They have no acute angles. G. They are both trapezoids. H. They both have four congruent angles. J. They both have four congruent sides. 7. Beth planted a garden in her backyard. What is the best name for the shape of the garden? A. Triangle B. Quadrilateral C. Pentagon D. Hexagon 8. Create a diagram or graphic organizer comparing the similarities and differences between quadrilaterals. Skills Checklist I can Compare and contrast attributes of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid. Identify the classification(s) to which a quadrilateral belongs, using deductive reasoning and inference. 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. HINTS & NOTES PRACTICE Translation = SLIDE 1. Translate the figure horizontally -3 units. Rotation = TURN
8 Clockwise = Counterclockwise = Horizontal = Vertical = Which best describes the location of the image of the vertex L? A. ( -1, -2) B. (2, -5) C. (5, -2) D. (2, 1) 2. Reflect XYZ over x- axis and write the new coordinates in the boxes provided.
9 3. Rotate rectangle ABCD 180, and sketch the new image. 4. William dilated triangle PQR by a scale factor on the coordinate plane to the right. Select the scale factor used. Skills Checklist I can Identify the coordinates of the image of a right triangle or rectangle that has been translated either vertically, horizontally, or a combination of a vertical and horizontal translation.
10 Identify the coordinates of the image of a right triangle or rectangle that has been rotated 90 or 180 about the origin. Identify the coordinates of the image of a right triangle or a rectangle that has been reflected over the x- or y-axis. Identify the coordinates of a right triangle or rectangle that has been dilated. The center of the dilation will be the origin. Sketch the image of a right triangle or rectangle translated vertically or horizontally. Sketch the image of a right triangle or rectangle that has been rotated 90 or 180 about the origin. Sketch the image of a right triangle or rectangle that has been reflected over the x- or y- axis. Sketch the image of a dilation of a right triangle or rectangle limited to a scale factor of
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